Problem: Rewrite as a simplified fraction. ${0.\overline{69} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 69.6969...\\ 1x &= 0.6969...\end{align*}}$ Subtracting the two equations, we have: ${99x = 69}$ ${x = \dfrac{69}{99}} $ ${x = \dfrac{23}{33}} $